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Chapter 24 Homework
Due: 8:00am on Wednesday, February 10, 2010
Note: To understand how points are awarded, read your instructor's Grading Policy.
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A Two-Lens System
A compound lens system consists of two converging lenses, one at
centimeter tall is placed at
with focal length
, and the other at
with focal length
. An object
.
Part A
What is the location of the final image produced by the compound lens system? Give the x coordinate of the image.
Hint A.1
How to handle multiple optics
Hint not displayed
Hint A.2
Find the object distance for the first lens
Hint not displayed
Hint A.3
Find the image distance from the first lens
Hint not displayed
Hint A.4
Find the object distance for the second lens
Hint not displayed
Hint A.5
Find the image distance from the second lens
Hint not displayed
Express your answer in centimeters, to three significant figures or as a fraction.
ANSWER:
= 31.8
Correct
Part B
How tall is the image?
Hint B.1
How to approach the problem
Hint not displayed
Hint B.2
Find the magnification of the first lens
Hint not displayed
Hint B.3
Find the magnification of the second lens
Hint not displayed
Express your answer in centimeters, to three significant figures or as a fraction.
ANSWER:
= 0.236
Correct
Part C
Is the final image upright or inverted, relative to the original object at
ANSWER:
?
upright
inverted
Correct
Now remove the two lenses at
and
and replace them with a single lens of focal length
at
. We want to choose this new lens so that it produces an image at the same
location as before.
Part D
What is the focal length of the new lens at the origin?
Hint D.1
Find the object distance for the third lens
Hint not displayed
Hint D.2
Find the image distance for the third lens
Hint not displayed
Express your answer in centimeters, to three significant figures or as a fraction.
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ANSWER:
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= 19.42
Correct
Part E
Is the image formed by
Hint E.1
the same size as the image formed by the compound lens system? Does it have the same orientation?
Find the magnification of the third lens
Hint not displayed
ANSWER:
The image is the same size and oriented the same.
The image is the same size and oriented differently.
The image is a different size and oriented the same.
The image is a different size and oriented differently.
Correct
Problem 24.5
A 1.3-
-tall object is 30
to the left of a lens with a focal length of 15
. A second lens with a focal length of -5
is 44
to the right of the first lens.
Part A
Calculate the distance between the image and the second lens.
Express your answer using two significant figures.
ANSWER:
= 3.7
Correct
Part B
Calculate the image height.
Express your answer using two significant figures.
ANSWER:
= 0.34
Correct
Problem 24.7
Part A
What is the -number of a lens with a 40
focal length and a 6.6-
-diameter aperture?
Express your answer using two significant figures.
ANSWER:
-number = 6.1
Correct
Nearsightedness and Farsightedness
A person with normal vision can focus on objects as close as a few centimeters from the eye up to objects infinitely far away. There exist, however, certain conditions under which the range of vision is not so
extended. For example, a nearsighted person cannot focus on objects farther than a certain point (the far point), while a farsighted person cannot focus on objects closer than a certain point (the near point). Note
that even though the presence of a near point is common to everyone, a farsighted person has a near point that is much farther from the eye than the near point of a person with normal vision.
Both nearsightedness and farsightedness can be corrected with the use of glasses or contact lenses. In this case, the eye converges the light coming from the image formed by the corrective lens rather than from the
object itself.
Part A
When glasses (or contact lenses) are used to correct nearsightedness, where should the corrective lens form an image of an object located at infinity in order for the eye to form a clear image of that object?
Hint A.1
Range of vision in nearsightedness
Hint not displayed
ANSWER:
The lens should form the image at the near point.
The lens should form the image at the far point.
The lens should form the image at a point closer to the eye than the near point.
The lens should form the image at a point farther from the eye than the far point.
Correct
This effect is achieved by the use of a diverging lens, as shown in the figure.
Part B
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If a nearsighted person has a far point
Hint B.1
that is 3.50
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from the eye, what is the focal length
of the contact lenses that the person would need to see an object at infinity clearly?
How to approach the problem
Hint not displayed
Hint B.2
Find the object distance
Hint not displayed
Hint B.3
Find the image distance
Hint not displayed
Express your answer in meters.
ANSWER:
= -3.50
Correct
Part C
When glasses (or contact lenses) are used to correct farsightedness, where should the corrective lens form an image of an object located between the eye and the near point in order for the eye to form a clear
image of that object?
Hint C.1
Range of vision in farsightedness
Hint not displayed
ANSWER:
The lens should form the image at the near point.
The lens should form the image at the far point.
The lens should form the image at a point closer to the eye than the near point.
The lens should form the image at a point farther from the eye than the far point.
Correct
This effect is achieved by the use of a converging lens, as shown in the figure.
Part D
If a farsighted person has a near point that is 0.600
Hint D.1
from the eye, what is the focal length
of the contact lenses that the person would need to be able to read a book held at 0.350
from the person's eyes?
How to approach the problem
Hint not displayed
Hint D.2
Find the object distance
Hint not displayed
Hint D.3
Find the image distance
Hint not displayed
Express your answer in meters.
ANSWER:
= 0.840
Correct
Problem 24.13
Ellen wears eyeglasses with the prescription -1.0
.
Part A
What eye condition does Ellen have?
ANSWER:
hyperopia
myopia
Correct
Part B
What is her far point without the glasses?
Express your answer using two significant figures.
ANSWER:
= 100
Correct
Problem 24.17
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A standardized biological microscope has an 8.0-
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-focal-length objective.
Part A
What focal-length eyepiece should be used to achieve a total magnification of
?
Express your answer using two significant figures.
ANSWER:
= 2.5
Correct
Problem 24.46
The Hubble Space Telescope has a mirror diameter of 2.4
.
. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650
Part A
What's the distance (in
) between two stars that are marginally resolved? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.
Express your answer using two significant figures.
ANSWER:
10
= 9.4×10
Correct
Part B
For comparison, what is this distance as a multiple of the distance of Jupiter from the sun?
Express your answer using two significant figures.
ANSWER:
= 120
Correct
Resolving Power of the Eye
If you can read the bottom row of your doctor's eye chart, your eye has a resolving power of one arcminute, equal to 1.67×10−2
.
Part A
If this resolving power is diffraction-limited, to what effective diameter of your eye's optical system does this correspond? Use Rayleigh's criterion and assume that the wavelength of the light is 550
Hint A.1
.
Definition of Rayleigh's criterion
Hint not displayed
Hint A.2
Diffraction equation for a circular aperature
Hint not displayed
Express your answer in millimeters to three significant figures.
ANSWER:
2.31
Correct
Score Summary:
Your score on this assignment is 99.9%.
You received 49.97 out of a possible total of 50 points.
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